Bush John W M, Couder Yves, Gilet Tristan, Milewski Paul A, Nachbin André
Department of Mathematics, MIT, Cambridge, Massachusetts 02139, USA.
Matière et Sytèmes Complexes, CNRS UMR 7057, Université Paris Diderot, Sorbonne Paris Cité, 75013 Paris, France.
Chaos. 2018 Sep;28(9):096001. doi: 10.1063/1.5055383.
Hydrodynamic quantum analogs is a nascent field initiated in 2005 by the discovery of a hydrodynamic pilot-wave system [Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Nature , 208 (2005)]. The system consists of a millimetric droplet self-propeling along the surface of a vibrating bath through a resonant interaction with its own wave field [J. W. M. Bush, Annu. Rev. Fluid Mech. , 269-292 (2015)]. There are three critical ingredients for the quantum like-behavior. The first is "path memory" [A. Eddi, E. Sultan, J. Moukhtar, E. Fort, M. Rossi, and Y. Couder, J. Fluid Mech. , 433-463 (2011)], which renders the system non-Markovian: the instantaneous wave force acting on the droplet depends explicitly on its past. The second is the resonance condition between droplet and wave that ensures a highly structured monochromatic pilot wave field that imposes an effective potential on the walking droplet, resulting in preferred, quantized states. The third ingredient is chaos, which in several systems is characterized by unpredictable switching between unstable periodic orbits. This focus issue is devoted to recent studies of and relating to pilot-wave hydrodynamics, a field that attempts to answer the following simple but provocative question:
流体动力学量子模拟是一个新兴领域，始于2005年对流体动力学导波系统的发现[Y. 库德、S. 普罗蒂埃、E. 福特和A. 布达乌德，《自然》，208 (2005)]。该系统由一个毫米级液滴组成，它通过与自身波场的共振相互作用，在振动浴的表面自行推进[J. W. M. 布什，《流体力学年度评论》，269 - 292 (2015)]。类量子行为有三个关键要素。第一个是“路径记忆”[A. 埃迪、E. 苏丹、J. 穆赫塔尔、E. 福特、M. 罗西和Y. 库德，《流体力学杂志》，433 - 463 (2011)]，这使得系统是非马尔可夫的：作用在液滴上的瞬时波力明确取决于其过去。第二个是液滴与波之间的共振条件，这确保了一个高度结构化的单色导波场，该场对行走的液滴施加有效势，从而产生优选的、量子化的状态。第三个要素是混沌，在几个系统中，混沌的特征是在不稳定周期轨道之间不可预测的切换。本焦点问题致力于对导波流体动力学的最新研究以及与之相关的研究，该领域试图回答以下简单但具有启发性的问题：
